FINAL EXAM
STAT 101, Instructors: A. Wyner, A. Rakhlin
December 15, 2009
Student Name:
Section:
Instructions
•
Use the space provided to answer questions. You can use the back of these pages
as scratch paper.
•
You must show work and give explanations (except for the multiplechoice questions).
•
Rules of uniformity: Onesided letter crib sheet, calculator ok (even with statistical functions
and graphing), otherwise closed notes, closed book.
•
No cell phones visible!
•
Rules of Fairness:
–
Complete this exam entirely on your own. Do not acquire information from other stu
dents or the outside in any form.
–
Do not take copies of this exam out of this room.
–
You have two hours for this exam. Any student observed continuing to write after time
has been called will be documented and points will be deducted.
•
Rules of Consideration:
–
Be considerate to others by not causing commotion and distraction.
–
If you ﬁnish early, leave quietly; avoid slamming doors.
Honor code applies to the above Rules.
Your signature:
About this test: When more than one choice seems reasonable, pick the one that is best.
STOP
WAIT UNTIL YOU ARE INSTRUCTED TO PROCEED.
19 questions for a total of 100 points.
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View Full DocumentSTAT 101
Final Exam
1. (2 points) If the sample size
n
is large and
p
is the population proportion, the
sampling distri
bution of the proportion
is approximately
(a) Binomial
Bin
(1
/
2
,p
)
(b) Normal
N
(
p,SD
(
X
i
))
(c)
Normal
N
(
p,p
(1

p
)
/n
)
(d) Normal
N
(ˆ
p,
ˆ
p
(1

ˆ
p
)
/n
)
(e) Normal
N
(
p,
p
p
(1

p
)
/n
)
2. (2 points) The Central Limit Theorem asserts that for i.i.d. random variables
X
1
,...,X
n
(a) The histogram of the data closely resembles the probability distribution of
X
i
when
n
is
large.
(b) The histogram of the data closely approximates the mean of the population when
n
is
large.
(c)
The sampling distribution of the mean is approximately normal when
n
is
large.
(d) The sampling distribution of the mean resembles the probability distribution of
X
i
.
3. (2 points) The probability distribution for the
average
of 9 i.i.d. normal
N
(2
,
3
2
) random
variables
X
1
,...,X
9
is best described as
(a) Approximately
N
(2
,
3
2
)
(b) Exactly
N
(2
,
3)
(c) Exactly
N
(1
/
9
,
3
2
/
9)
(d)
Exactly
N
(2
,
1)
(e) Can only be determined if the distribution of
X
i
is known since the smaple size
n
is only
9.
4. (2 points) A sample of size 80 produces a conﬁdence interval of length 2. To make the length
of the interval equal to 1, we can
(a) Increase sample size by an additional 4 points (84 total)
(b) Change control limits to decrease Type I error
(c) Decrease sample size by a factor of 4 (20 total)
(d)
Increase sample size by a factor of 4 (320 total)
5. (2 points) A given sample yields a 95% conﬁdence interval [5
,
10] for the population mean
μ
.
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 Fall '08
 Heller
 Statistics, Professor Rakhlin

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